Robinson expects the veteran winger to make a call on his future in the next "two to three weeks" as he nurses a shoulder injury that will sideline him until round 27.
With 302 appearances to his name, three-time premiership winner Tupou should overtake Jared Waerea-Hargreaves (310) and become the foundation club's most-capped player if he re-signs for 2027.
But after a mostly fortunate run of fitness across his 15 NRL seasons, Tupou spent two months out with a calf injury earlier in the year before dislocating his shoulder against Newcastle last week.
Robinson suggested on Tuesday the injuries were "innocuous", but was unsure whether it would factor into the 35-year-old's deliberations over his future.
"I'm not sure is the answer. I don't know," he said.
"Toops is an honest man, he's quite clear about that and he's not going to fake it. He'll make a decision whether he's ready to go or whether he's not.
"So, I'm not sure whether that (injury) will shift that last week.
"I'd say it'd be in the next two to three weeks we'll know where Toops is at and where we're at."
The Roosters want to keep Tupou, and no one more so than Robinson.
One of Robinson's first major selection decisions on joining the Roosters for the 2013 season was to decide on Tupou as the winner of a selection battle with the more-experienced Michael Oldfield.
Tupou went on to become a regular first-grader for the first time under Robinson that year, and is the last player remaining at the club from the 2013 premiership triumph.
He remains an elite aerial threat on the wing, and is just as valued by Robinson for his leadership.
"There's guys in the change room that make other guys feel good," Robinson said.
"We obviously had a few of those guys at different times: Boyd Cordner, Jared Waerea-Hargreaves. Toops is one of those where when he's there you go, 'Okay, I know what he's going to do now. What are the rest of us going to do?'
"You don't always get that luxury."
Journeyman Tommy Talau appears the likeliest candidate to replace Tupou on the wing against North Queensland on Thursday night.
Queensland prop Lindsay Collins will miss the trip to Townsville, still sidelined with the concussion he suffered against Brisbane on June 26.
Collins, who has a history of head knocks, has resumed training but not contact work.
"He's going well, but it'll be in the next couple of weeks he'll get back on the field," Robinson said.
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